Abstract [en]

The Ramachandran angles (phi, psi) of a protein backbone form the vertices of a piecewise geodesic curve on the surface of a torus. When the ends of the curve are connected to each other similarly, by a geodesic, the result is a closed string that in general wraps around the torus a number of times both in the meridional and the longitudinal directions. The two wrapping numbers are global characteristics of the protein structure. A statistical analysis of the wrapping numbers in terms of crystallographic x-ray structures in the protein data bank (PDB) reveals that proteins have no net chirality in the phi direction but in the psi direction, proteins prefer to display chirality. A comparison between the wrapping numbers and the concept of folding index discloses a non-linearity in their relationship. Thus these three integer valued invariants can be used in tandem, to scrutinize and classify the global loop structure of individual PDB proteins, in terms of the overall fold topology.